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Publications (32)
Problem posing is a promising teaching method for enhancing motivation and performance in mathematics and more specifically in mathematical modelling. Hence, the goals of our study were twofold: (1) to examine the effects of problem posing on modelling performance, self-efficacy, and task values in solving modelling problems, and (2) to analyze whe...
Das Anfertigen einer Skizze ist eine leistungsstarke Strategie beim mathematischen Problemlösen, wirkt sich jedoch bei nicht linearen Geometrieproblemen negativ auf die Leistung der Lernenden aus. (De Bock et al., 2007; Krawitz & Schukajlow, 2020). Die Reanalyse der Daten der Studie von Krawitz & Schukajlow (2020) hat ergänzend zu schon bekannten B...
Problem Posing gilt als vielversprechende Methode und als eigenständiges
Lernziel, doch die Konzeptualisierung und Messung sind weitestgehend ungeklärt.
Ziel der Studie (N = 116 Neunt- und Zehntklässler:innen) ist die Validierung eines Instruments zum modellierungsbezogenen Problem Posing. Untersucht wird die Struktur des Problem Posings und der Zu...
Recent research has shown that problem-posing prompts affect students' achievement-related outcomes in problem-posing tasks. This study extends such findings by investigating the effects of problem-posing prompts on students' motivational outcomes. Ninth-and tenth-graders (N = 78) were prompted to pose easy and difficult problems. Subsequently, eac...
Task values are important for learning. However, prior research has indicated a lack of studies that have addressed students' task values in mathematics. In the following study (N = 293), we analyzed (1) the relationships between intrinsic, attainment, and utility values and (2) how teaching students to solve open modelling problems affects these v...
Based on expectancy-value theory, this study adopted a person-centred approach to explore the heterogeneous profiles of secondary German and Taiwanese students’ mathematical modelling task values, and examined the differences in their mathematical modelling performance, controlling for the variable of intra-mathematical knowledge among the heteroge...
One characteristic feature of modelling problems is their openness. In current research, there is a lack of theoretical and empirical information on how to deal with the openness of modelling problems in the classroom. In this chapter, we summarise research on open problems and present a process model for dealing with modelling problems with a spec...
Problem posing-generating one's own problems-is considered a powerful teaching approach for fostering students' motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students' interest is largely missing. In this contribution, we present a study with 105 ninth-and tenth-grader...
Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these...
In mathematics education, pre-formulated modelling problems are used to teach mathematical modelling. However, in out-of-school scenarios problems have to be identified and posed often first before they can be solved. Despite the ongoing emphasis on the activities involved in solving given modelling problems, little is known about the activities in...
Experiences of competence and autonomy are essential for intrinsic motivation, social development, and well-being. However, little is known about how these constructs are related to previous achievement in mathematics. In the present study, we investigated whether ninth-graders (N = 83) with different levels of achievement differ in their experienc...
Das OModA-Projekt (Offene Modellierungsaufgaben in einem selbstständigkeitsorientierten Mathematikunterricht) verfolgt die Fragestellung, welche Effekte eine Lernumgebung mit offenen Modellierungsaufgaben im Vergleich zu geschlossenen Modellierungsaufgaben auf Motivation und Leistung hat. Hierzu wurde eine Lernumgebung konzipiert, die in diesem Bei...
Während das Anfertigen einer Skizze im Allgemeinen als leistungsstarke
Strategie zur Lösung mathematischer Probleme gilt, stellten De Bock et al.
(2003) überraschenderweise fest, dass sich das Zeichnen einer Skizze negativ
auf die Leistung von Lernenden beim Lösen von Aufgaben zu nicht-linearen
Geometrieproblemen auswirkt. Als wichtigen Grund für d...
In real life, problems emerge from situations and often need to be posed before they can be solved. Despite the ongoing emphasis on the processes involved in solving modelling problems, little is known about the process of problem posing. To help fill this gap, the current study examined (1) what activities are involved in modelling-related problem...
Modelling is an important part of mathematical learning. One characteristic feature of modelling problems is their openness. In this study, we investigated the relationship between interest and performance in solving open modelling problems and closed real-
world problems. We used questionnaires and tests to assess the interest and performance of 1...
Making realistic assumptions is an important part of solving open modelling problems and also a potential source of errors. But little is known about the difficulties that result from the openness of modelling problems and how they can be addressed in interventions. Here, we focus on two central solution steps that are necessary for making assumpti...
To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelli...
In diesem Beitrag berichten wir über eine methodisch-inhaltliche Lehrinnovation in der Fachvorlesung „Arithmetik für die Grundschule“ an der Universität Kassel und deren Untersuchung im Rahmen des KLIMAGS-Projekts. Die Untersuchung evaluierte Wirkungen der Innovation in einem Vortest-Nachtest-Design mit Experimental- und Kontrollgruppe (n = 131). D...
As problem posing has been shown to foster students’ problem-solving abilities, problem posing might serve as an innovative teaching approach for improving students’ modelling performance. However, there is little research on problem posing regarding real-world situations. The present paper addresses this research gap by using a modelling perspecti...
Make a drawing is known to be a powerful strategy for solving mathematical
problems. But surprisingly, the drawing strategy was found to negatively affect
the ability to solve non-linear geometry problems. Our study replicates and
extends this finding by addressing the quality of the drawing strategy, which
might explain the negative effect. In a r...
The strategy of making a drawing has been claimed to facilitate mathematical problem solving. However, De Bock et al. (2003) surprisingly found that drawing negatively affected performance in solving non-linear geometry problems, in which the area or volume of similar figures or solids had to be determined by a given scaling factor. The authors sug...
Um erfolgreich modellieren zu können, muss Vorwissen über mathematische und realitätsbezogene Sachverhalte verknüpft und sinnbringend zum Lösen eines Problems eingesetzt werden. Janina Krawitz untersucht mit inhaltsanalytischen Methoden, wie sich die Aktivierung verschiedenen Vorwissens auf die Lösungsprozesse von mathematischen Modellierungsaufgab...
Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In thi...
It is a well-documented finding that students tend to neglect their real-world knowledge when solving word problems, even when realistic assumptions are needed. Although studies have successfully shown the extent to which students tend to provide unrealistic responses, the question of where this tendency comes from has yet to be answered. We focuse...
In a qualitative study with eighth to tenth graders (N=18), we investigated whether the activation of prior mathematical knowledge would promote or interfere with solution processes as students solved modelling problems. In addition, we analyzed the role of metacognitive monitoring of knowledge activation. Participants with different prior mathemat...
Posing modelling problems in class is supposed to increase students’ motivation. As motivation is assumed
to emerge from task value and self-efficacy expectations, the present study considered both constructs with the aims to examine (1) whether students have different values and self-efficacy expectations concerning modelling problems versus dres...
In an experimental study with ninth graders (N=165), we investigated whether
presenting reading comprehension prompts would have a positive impact on
students’ enjoyment and performance in modelling. Contrary to our expectations, the
enjoyment and modelling performance of students who received reading
comprehension prompts were similar to those of...
Since 2009 in Germany the Lernstandserhebungen are written, among others, in mathematics in Grade 8. These tests are also called “Vergleichsarbeiten” or “VerA-8”. By using these tests teachers get an orientation and are given the possibility of a competence-centered diagnoses of their pupils, followed by an individual enhancement and a quality deve...
